Related papers: The Riemann problem of relativistic Euler system w…
Synge's problem consists in to determine the dynamics of two point electrical charges interacting through their electromagnetic fields, without to take into account the radiation terms due to the self-forces in each charge. We discuss how…
A mathematical complication due to an unnecessary formal assumption concerning the variational principle of general relativity theory, which apparently bothered Einstein and Hilbert, is shown and cleared up. Some historical confusion seems…
A number of well-known difficulties in physics resulted from merging the theory of relativity with the Compton-de Broglie wave mechanics. Two such problems were the failure of Dirac's relativistic wave equation to predict the correct…
The problem of the electromagnetic radiation of an accelerated charged particle is one of the most controversial issues in Physics since the beginning of the last century, representing one of the most popular unsolved problems of the Modern…
In this paper, the compressible Euler system with velocity alignment and damping is considered, where the influence matrix of velocity alignment is not positive definite. Sound speed is used to reformulate the system into symmetric…
We consider diatomic systems in which the kinetic energy of the electrons is treated in a simple relativistic model. The Born-Oppenheimer approximation is assumed. We investigate questions of stability, deducing bounds on the number $N$ of…
We show that the invariant measure of point vortices, when conditioning the Hamiltonian to a finite interval, converges weakly to the enstrophy measure by conditioning the renormalized energy to the same interval. We also prove the…
The motion of a continuum of matter subject to gravitational interaction is classically described by the Euler-Poisson system. Prescribing the density of matter at initial and final times, we are able to obtain weak solutions for this…
We are concerned with the large time behavior of solutions to the Cauchy problem of the one-dimensional compressible micropolar fluid model without viscosity, where the far-field states of the initial data are prescribed to be different. If…
In recent years, there has been some interest in applying ideas and methods taken from Physics in order to approach several challenging mathematical problems, particularly the Riemann Hypothesis. Most of these kind of contributions are…
In the present article, a modified Cauchy problem (problem C) for the hyperbolic equation of the third order with the data on the equation's coefficients singularity plane is solved by Riemann method. The special class in which the solution…
It is shown, that the conventional presentation of the Maxwell equations for the electromagnetic field in the Riemannian space-time appears to be problematic. The reason of hesitations is the fact, that a solution of the Maxwell equations…
Classical relativistic system of point particles coupled with an electromagnetic field is considered in the three-dimensional representation. The gauge freedom connected with the chronometrical invariance of the four-dimensional description…
Considering the isentropic Euler equations of compressible fluid dynamics with geometric effects included, we establish the existence of entropy solutions for a large class of initial data. We cover fluid flows in a nozzle or in spherical…
In this paper, we study the regularity properties of bounded entropy solutions to the isentropic Euler equations with $\gamma = 3$. First, we use a blow-up technique to obtain a new trace theorem for all such solutions. Second, we use a…
We study Neumann functions for divergence form, second order elliptic systems with bounded measurable coefficients in a bounded Lipschitz domain or a Lipschitz graph domain. We establish existence, uniqueness, and various estimates for the…
We establish the existence of global weak solutions of the 2D incompressible Euler equation, for a large class of non-smooth open sets. These open sets are the complements (in a simply connected domain) of a finite number of connected…
In this article, we develop a new hyperbolic model governing the first-order dynamics of a thin film flow under the influence of gravity and solute transport. The obtained system turns out to be a non-symmetric Keyfitz-Kranzer type system.…
For nonlinear hyperbolic systems of conservation laws in one space variable, we establish the existence of nonclassical entropy solutions exhibiting nonlinear interactions between shock waves with strong strength. The proposed theory is…
These lecture notes provide the material for a short introductory course on effective equations for classical particle systems. They concern the basic equations in kinetic theory, written by Boltzmann and Landau, describing rarefied gases…